Methods exist for inserting a preceding element i−1 and then a following element i in the ground along a calculated path in order to construct a work using an inserter arm that is guided in displacement. Those prior methods comprise:
a step of establishing nominal positions at which the elements are to be inserted in the ground as a function of the calculated path; and
a guidance step of automatically guiding the inserter arm towards a target position at which the following element is to be inserted as a function of the nominal position established for the following element and as a function of topographical readings.
By way of example, those methods are used for inserting base plates in concrete slabs for supporting the rails of a railway track. In particular, this is used for making railway tracks that have no ballast or no sleepers (ties). For example, such insertion methods are described in European patent applications EP 0 803 609 and EP 1 178 153.
The inserter arm must be placed above the ground with great accuracy. To do this, it is known to control the displacement of the arm as a function of topographical readings (see EP 1 178 153).
Those methods give satisfaction. In particular, they make it possible to position each element with absolute error that is small relative to the nominal position at which the element should have been inserted. The term “absolute positioning error of the element i” is used herein to mean the difference Dai between the position of coordinates Xmi, Ymi, and Zmi at which the element i is actually inserted in the ground and the nominal position of coordinates Xni, Yni, and Zni that was established for the element. By way of example, existing methods make it possible to keep the absolute error within a range of ±1 millimeter (mm). It is then said that the absolute accuracy of the method is ±1 mm.
With such absolute accuracy, the relative error Dri between the element i−1 and the element i lies in a range that is twice as great as that which is acceptable for the absolute error. The term relative error Dri for the positioning between the element i−1 and the element i is used to mean the difference between the absolute error Dai in the positioning of the element i and the absolute error Dai−1 in the positioning of the element i−1.
With railway tracks, the absolute error is kept within bounds so as to ensure that the passengers of the train cannot feel troublesome vibration. Existing methods enable that objective to be achieved.
Nevertheless, in existing methods, nothing is done to reduce relative positioning error. Thus, in an extreme case, the following situation could occur. The element i−1 presents an absolute error of +1 mm in one direction and the element i presents an absolute error of −1 mm in the same direction. Each of these two absolute errors lies within the range of absolute errors that are acceptable. Nevertheless, under such conditions, the relative error Dri is equal to 2 mm, which may be considered as being unacceptable, since for example that might lead to troublesome vibration for passengers.
It is therefore desirable to reduce the relative error.